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In '''functional notation''', a ], as a ], is combined with another which is regarded as a symbol of ]. Thus <math>f(x)</math> denotes the ] of the performance of the operation <math>f</math> upon the ] <math>x</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> If upon this result the same operation were repeated, the new result would be expressed by <math>f</math>, or more concisely by <math>f^2(x)</math>, and so on. The quantity <math>x</math> itself regarded as the result of the same operation <math>f</math> upon some other function; the proper symbol for which is, by analogy, <math>f^{-1} (x)</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> Thus <math>f</math> and <math>f^{-1}</math> are symbols of ]s, the former cancelling the effect of the latter on the subject <math>x</math>. <math>f(x)</math> and <math>f^{-1} (x)</math> in a similar manner are termed ]s.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> In '''functional notation''', a ], as a ], is combined with another which is regarded as a symbol of ]. Thus <math>f(x)</math> denotes the ] of the performance of the operation <math>f</math> upon the ] <math>x</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> If upon this result the same operation were repeated, the new result would be expressed by <math>f</math>, or more concisely by <math>f^2(x)</math>, and so on. The quantity <math>x</math> itself regarded as the result of the same operation <math>f</math> upon some other function; the proper symbol for which is, by analogy, <math>f^{-1} (x)</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> Thus <math>f</math> and <math>f^{-1}</math> are symbols of ]s, the former cancelling the effect of the latter on the subject <math>x</math>. <math>f(x)</math> and <math>f^{-1} (x)</math> in a similar manner are termed ]s.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref>


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In functional notation, a letter, as a symbol of operation, is combined with another which is regarded as a symbol of quantity. Thus f ( x ) {\displaystyle f(x)} denotes the mathematical result of the performance of the operation f {\displaystyle f} upon the subject x {\displaystyle x} . If upon this result the same operation were repeated, the new result would be expressed by f [ f ( x ) ] {\displaystyle f} , or more concisely by f 2 ( x ) {\displaystyle f^{2}(x)} , and so on. The quantity x {\displaystyle x} itself regarded as the result of the same operation f {\displaystyle f} upon some other function; the proper symbol for which is, by analogy, f − 1 ( x ) {\displaystyle f^{-1}(x)} . Thus f {\displaystyle f} and f − 1 {\displaystyle f^{-1}} are symbols of inverse operations, the former cancelling the effect of the latter on the subject x {\displaystyle x} . f ( x ) {\displaystyle f(x)} and f − 1 ( x ) {\displaystyle f^{-1}(x)} in a similar manner are termed inverse functions.

References

  1. A dictionary of science, literature and art, ed. by W.T. Brande. Pg 683
  2. A dictionary of science, literature and art, ed. by W.T. Brande. Pg 683
  3. A dictionary of science, literature and art, ed. by W.T. Brande. Pg 683
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